Promising regimes for the observation of topological degeneracy in spin chains

Both the Haldane spin chain and a topologically dimerized chain feature topologically protected edge states that are expected to be robust against some kind of noise. To elucidate whether it might be feasible to create such edge states in dimerized chains in a controlled manner in solid states environments, e.g., as spin chains on surfaces, as has already been successfully achieved with the Haldane chain, we investigate their robustness with respect to long-range coupling, anisotropies, and finite chain length. The theoretical investigation is based on an alternating Heisenberg spin chain with spin-$1/2$, which is investigated using exact diagonalization. We find that dimerized chains and Haldane chains have robustness against long-range coupling and anisotropies. In particular, dimerized spin chains are significantly more robust than Haldane chains.